Electron travels on a circular orbit in a way that de Broglie wave
is a standing one - position of arrows are constant.
Like the vibrating wine glass
or a "Chinese" bowl
The bowl can also vibrate making not 4 but 6
arrows on the circle -
it "plays" not its first (fundamental) but higher harmonics
.
For the hydrogen atom this would be the third orbit.
Obviosly, the bowl is not the best instuments to hear clearly harmonics-
try the first and second harmonics
of this flute. Try violin
and see its frequency spectrum
.
Very simple! It is just a single tube with gas and two mirrors on ends.
To make it "singing" at a certain frequency (color) it is just enough to adjust the length of the tube to the wavelength of the light (i.e. to its multiple).
Exactly the same, as this didgeridoo player [1] does.
Very, very recent lasers, allowing to observe single electron in flight
[2] emmit ultrafast puleses, which are, due to Heisenberg principle, not any
more of well defined color but white. Like "white" is this sound [3] .
If you don't believe, just watch this sound!
[1] “Fruits fo the Forest” from “Didgeridoo, Tribal Spirit”
by Tjnara Goreng-Goreng, Simon Black plays on didgeridoo, Mazur Media,
2002
[2] J. Itani et al., Tomographic imaging of molecular orbitals, Nature 432
(Dec. 2004) 867
[3] Fryderyk Chopin, Impromptu cis-moll op.posth., plays Rafał Lewandowski,
Futurex, 2001